Albert Einstein: Notes for an Autobiography

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Notes for an Autobiography

ALBERT EINSTEIN

Editor's Note: Ajter resisting countless eijorts over many
years to persuade him to write about his life, Dr, Albert
Einstein has finally written a short autobiographical
memoir centered around the development of his ideas. A
fairly substantial portion of that memoir is published
herewith. The editors are deeply grateful to Dr. Einstein
and Dr. Paul Arthur Schilpp, of Northwestern University,
for the privilege of running the essay in SRL. The memoir
was written at the suggestion of Professor Schilpp, who
has translated it from the German. The entire work will
be published shortly by the Library of Living Philoso-
phers, Inc,, of Evanston, 111., under the title ''Albert Ein-
stein: Philosopher-Scientist/'

Some of the material that follows is highly technical
and requires advanced knowledge, but the editors believed
that to withhold publication in SRL on this account would
deprive our readers of a publishing event of importance.

HERE I sit in order to write, at the age of sixty-
seven, something like my own obituary. I am
doing this because I believe that it is a good
thing to show those who are striving alongside us
how one*s own striving and searching appear to one in
retrospect. After some reflection, I felt how insufficient
any such attempt is bound to be. For, however brief and
limited one's working life may be, and however pre-
dominant may be the ways of error, the exposition of
that which is worthy of communication does nonetheless
not come easy — today's person of sixty-seven is by no
means the same as was the one of fifty, of thirty, or of
twenty. Every reminiscence is colored by today's being
what it is, and therefore by a deceptive point of view.
This consideration could very well deter. Nevertheless
much can be lifted out of one's own experience which is
not open to another consciousness.

Even when I was a fairly precocious young man the
nothingness of the hopes and strivings which chase
most men restlessly through life came to my conscious-
ness with considerable vitality. Moreover, I soon dis-
covered the cruelty of that chase, which in those years
was much more carefully covered up by hypocrisy and
glittering words than is the case today. By the mere ex-
istence of his stomach everyone was condemned to par-
ticipate in that chase. Moreover, it was possible to satisfy
the stomach by such participation, but not man in so far
as he is a thinking and feeling being. As the first way
out there was religion, which is implanted into every
child by way of the traditional education-machine. Thus
I came— despite the fact that I was the son of entirely
irreligious (Jewish) parents—to a deep religiosity, which,
however, found an abrupt ending at the age of twelve.
Through the reading of popular scientific books I soon
reached the conviction that much in the stories of the

Bible could not be true. The consequence was a positively
fanatic orgy of freethinking coupled with the impression
that youth is intentionally being deceived by the state
through lies; it was a crushing impression. Suspicion
against every kind of authority grew out of this expe-
rience, a skeptical attitude towards the convictions which
were alive in any specific social environment — an atti-
tude which has never again left me, even though later on,
because of a better insight into the causal connections, it
lost some of its original poignancy.

It is quite clear to me that the religious paradise of
youth, which was thus lost, was a first attempt to free
myself from the chains of the "merely-personal," from
an existence which is dominated by wishes, hopes, and
primitive feelings. Out yonder there was this huge world,
which exists independently of us human beings and
which stands before us like a great, eternal riddle, at
least partially accessible to our inspection and thinking.
The contemplation of this world beckoned like a libera-
tion, and I soon noticed that many a man whom I had
learned to esteem and to admire had found inner free-
dom and security in devoted occupation with it. The
mental grasp of this extra-personal world within the
frame of the given possibilities swam as the highest aim
half consciously and half unconsciously before my mind's
eye. Similarly motivated men of the present and of the
past, as well as the insights which they had achieved,
were the friends which could not be lost. The road to
this paradise was not as comfortable and alluring as the
road to the religious paradise; but it has proved it-
self as trustworthy, and I have never regretted having
chosen it.

WHAT I have here said is true only within a certain
sense, just as a drawing consisting of a few strokes
can do justice to a complicated object, full of perplexing
details, only in a very limited sense. If an individual
enjoys well-ordered thoughts, it is quite possible that
this side of his nature may grow more pronounced at the
cost of other sides and thus, may determine his mentality
in increasing degree. In this case it is well possible that
such an individual in retrospect sees a uniformly syste-
matic development, whereas the actual experience takes
place in kaleidoscopic particular situations. The mani-
foldness of the external situations and the narrowness
of the momentary content of consciousness bring about
a sort of atomizing of the life of every human being. In
a man of my type the turning-point of the development
lies in the fact that gradually the major interest dis-
engages itself to a far-reaching degree from the momen-
tary and the merely personal and turns towards the
striving for a mental grasp of things.

What, precisely, is "thinking"? When, at the reception
of sense-impressions, memory-pictures emerge, this is

NOVEMBER 26, 1949

9

not yet "thinking." And when such pictures form series,
each member of which calls forth another, this, too, is
not yet "thinking." When, however, a certain picture
turns up in many such series, then — precisely through
such return — it becomes an ordering element for such
series, in that it connects series which in themselves are
unconnected. Such an element becomes an instrument,
a concept- I think that the transition from free associa-
tion or "dreaming" to thinking is characterized by the
more or less dominating role which the ^'concept'' plays
in it. It is by no means necessary that a concept must
be connected with a sensorily cognizable and reproducible
sign (word); but when this is the case thinking becomes
by means of that fact communicable.

With' what right — the reader will ask — doe^ this man
operate so carelessly and primitively with ideas in such
a problematic realm without making even the least effort
to prove anything? My defense: all our thinking is of
this nature of a free play with concepts; the justification
for this play lies in the measure of survey over the ex-
perience of the senses which we are able to achieve with
its aid. The concept of "truth" can not yet be applied to
such a structure; to my thinking this concept can come
in question only when a far-reach-
ing agreement (convention) con-
cerning the elements and rules of
the game is already at hand.

For me it is not dubious that our
thinking goes on for the most part
without use of signs (words) and
beyond that to a considerable
degree unconsciously. For how,
otherwise, should it happen that
sometimes we "wonder" quite
spontaneously about some experi-
ence? This "wondering" seems to
occur when an experience comes
into conflict with a world of con-
cepts which is already sufficiently
fixed in us. Whenever such a con-
flict is experienced hard and in-
tensively it reacts bacl<: upon our thought world in a de-
cisive way. The development of this thought world is in a
certain sense a continuous flight from "wonder."

A wonder of such nature I experienced as a child of
four or five years, when my father showed me a com-
pass. That this needle behaved in such a determined way
did not at all fit into the nature of events which could
find a place in the unconscious world of concepts (effect
connected with direct "touch"). I can still remember —
or at least believe I can remember — that this experience
made a deep and lasting impression upon me. Some-
thing deeply hidden had to be behind things. What man
sees before him from infancy causes no reaction of this
kind; he is not surprised over the falling of bodies, con-
cerning wind and rain, nor concerning the differences be-
tween living and non-living matter.

At the age of twelve I experienced a second wonder of
a totally different nature: in a little book dealing with
Euclidian plane geometry, which came into my hands at
the beginning of a school year. Here were assertions, as
for example the intersection of the three altitudes of a
triangle in one point, which — though by no means evi-
dent — could nevertheless be proved with such certainty
that any doubt appeared to be out of the question. This
lucidity and certainty made an indescribable impression
upon me. That the axiom had to be accepted unproved
did not disturb me. In any case it was quite sufficient for
me if I could peg proofs upon propositions the validity
of which did not seem to me to be dubious. For example,
I remember that an uncle told me the Pythagorean

theorem before the holy geometry booklet had come into
my hands. After much effort I succeeded in "proving"
this theorem on the basis of the similarity of triangles;
in doing so it seemed to me "evident" that the relations
of the sides of the right-angled triangles would have to
be completely determined by one of the acute angles.
Only something which did not in similar fashion seem to
be "evident" appeared to me to be in need of any proof
at all. Also, the objects with which geometry deals
seemed to be of no different type than the objects of
sensory perception, "which can be seen and touched."
This primitive idea, which probably also lies at the bot-
tom of the well-known Kantian problematic concerning
the possibility of "synthetic judgments a priori" rests
obviously upon the fact that the relation of geometrical
concepts to objects of direct experience (rigid rod, finite
interval, etc.) was unconsciously present.

If thus it appeared that it was possible to get certain
knowledge of the objects of experience by means of pure
thinking, this "wonder" rested upon an error. Neverthe-
less, for anyone who experiences it for the first time, it
is marvelous enough that man is capable at all of reaching
such a degree of certainty and purity in pure thinking as
the Greeks showed us for the first
time to be possible in geometry.

From the age of twelve to six-
teen I familiarized myself with the
elements of mathematics together
with the principles of differential
and integral calculus. In doing so
I had the good fortune of hitting
upon books which were not too
particular in their logical rigor, but
which made up for this by permit-
ting the main thoughts to stand out
clearly and synoptically. This oc-
cupation was, on the whole, truly ,
fascinating; climaxes were reached
whose impression could easily com-
pete with that of elementary geo-
metry—the basic idea of analytical
geometry, the infinite series, the concepts of differential
and integral. I also had the good fortune of getting to
know the essential results and methods of the entire field
of the natural sciences in an excellent popular exposi-
tion, which limited itself almost throughout to qualitative
aspects (Bernstein's "People's Books on Natural Science,"
a work of five or six volumes), a work which I read with
breathless attention. I had also already studied some
theoretical physics v/hen, at the age of seventeen, I en-
tered the Polytechnic Institute of Zurich.

There I had excellent teachers (for example, Hurwitz,
Minkowski), so that I really could have gotten a sound
mathematical education. However, I worked most of the
time in the physical laboratory, fascinated by the direct
contact with experience. The balance of the time I used
in the main in order to study at home the works of
Kirchhoff, Helmholtz, Hertz, etc. The fact that I neglected
mathematics to a certain extent had its cause not merely
in my stronger interest in the natural sciences than in
mathematics but also in the following strange experience,
I saw that mathematics was split up into numerous
specialities, each of which could easily absorb the short
lifetime granted to us. Consequently I saw myself in the
position of Buridan's ass, which was unable to decide
upon any specific bundle of hay. This was obviously due
to the fact that my intuition was not strong enough in
the field of mathematics in order to differentiate clearly
the fundamentally important, that which is really basic,
from the rest of the more or less dispensable erudition.
Beyond this, however, my interest in the knowledge

10

iTie Saturday Review

Einstein

of nature was also unqualifiedly
stronger; and it was not clear to me as
a student that the approach to a more
profound knowledge of the basic
principles of physics is tied up with the
most intricate mathematical methods.
This dawned upon me only gradually
after years of independent scientific
work. True enough, physics also was
divided into separate fields, each of
which was capable of devouring a short
lifetime of work without having satis-
fied the hunger for deeper knowledge.
The mass of insufficiently connected ex-
perimental data was overwhelming
here also. In this field, however, I soon
learned to scent out that which was
able to lead to fundamentals and to
turn aside from everything else, *from
the multitude of things which clutter
up the mind and divert it from the es-
sential. The hitch in this was, of course,
that one had to cram all this stuff
into one's mind for the examinations.

This coercion had such a deterring
effect (upon me) that, after I had
passed the final examination, I found the consideration of
any scientific problems distasteful to me for an entire
year. In justice I must add, moreover, that in Switzer-
land we had to suffer far less under such coercion,
which smothers every truly scientific impulse, than
is the case in many another locality. There were alto-
gether only two examinations; aside from these, one
could just about do as one pleased. This was especially
the case if one had a friend, as had I, who attended the
lectures regularly and who worked over their content
conscientiously. This gave one freedom in the choice of
pursuits until a few months before the examination, a
freedom which I enjoyed to a great extent and have
gladly taken into the bargain the bad conscience con-
nected with it as by far the lesser evil. It is, in fact,
nothing short of a miracle that the modern methods
of instruction have not yet entirely strangled the
holy curiosity of inquiry; for this delicate little plant,
aside from stimulation, stands mainly in need of
freedom; without this it goes to wrack and ruin without
fail.

TVTOW to the field of physics as it presented itself at that
^time. In spite of all the fruitfulness in particular,
dogmatic rigidity prevailed in matters of principles: in
the beginning (if there was such a thing) God created
Newton's laws of motion together with the necessary
masses and forces. This is all; everything beyond this
follows from the development of appropriate mathemati-
cal methods by means of deduction. What the nineteenth
century achieved on the strength of this basis, especially
through the application of the partial differential equa-
tions, was bound to arouse the admiration of every re-
ceptive person. Newton was probably first to reveal, in
his theory of sound-transmission, the efficacy of partial
differential equations. Euler had already created the
foundation of hydrodynamics. But the more precise de-
velopment of the mechanics of discrete masses, as the
basis of all physics, was the achievement of the nine-
teenth century.

What made the greatest impression upon the student,
however, was less the technical construction of mechanics
or the solution of complicated problems than the achieve-
ments of mechanics in areas which apparently had noth-
ing to do with mechanics: the mechanical theory of

— From *' Albert Einstein: A Biogrwphy for Young People."
at seven- — a keepsake now in his Princeton library,

light, which conceived of light as the wave-motion of a
quasi -rigid elastic ether, and above all the kinetic theory
of gases: the independence of the specific heat of mon-
atomic gases of the atomic weight, the derivation of the
equation of state of a gas and its relation to the specifir'
heat, the kinetic theory of the dissociation of gases, and
above all the quantitative connection of viscosity, heat-
conduction, and diffusion of gases, which also furnished
the absolute magnitude of the atom.

These results supported at the same time mechanics
as the foundation of physics and of the atomic hypothesis,
which latter was already firmly anchored in chemistry.
However, in chemistry only the ratios of the atomic
masses played any role, not their absolute magnitudes,
so that atomic theory could be viewed more as a visual-
izing symbol than as knowledge concerning the factual
construction of matter. Apart from this it was also of
profound interest that the statistical theory of classical
mechanics was able to deduce the basic laws of thermo-
dynamics, something which was in essence' already ac-
complished by Boltzmann.

We must not be surprised, therefore, that, so to speak,
all physicists of the last century saw in classical me-
chanics a firm and final foundation for all physics, yes,
indeed, for all natural science, and that they never grew
tired in their attempts to base Maxwell's theory of elec-
tro-magnetism, which in the meantime was slowly begin-
ning to win out, upon mechanics as well. Even Maxwell
and H. Hertz, who in retrospect appear as those who
demolished the faith in mechanics as the final basis of
all physical thinking, in their conscious thinking ad-
hered throughout to mechanics as the secured basis of
physics.

It was Ernst Mach, who, in his "History of Mechanics,"
shook this dogmatic faith; this book exercised a profound
influence upon me in this regard while I was a student. -
I see Mach's greatness in his incorruptible skepticism
and independence; in my younger years, however, Mach's
epistemological position also influenced me very greatly,
a position which today appears to me to be essentially
untenable. For he did not place in the correct light the
essentially constructive and speculative nature of thought
and more especially of scientific thought; in consequence
of which he condemned theory on precisely those points
where its constructive-speculative character unconceala-

NOVEMBER 26, 1949

11

bly comes to light, as, for example, in the kinetic atomic
theory.

"Is this supposed to be an obituary?" the astonished
reader will likely ask. I would like to reply: essentially
3'es. For the essential in the being of a man of my type
lies precisely in what he thinks and how he thinks, not
in what he does or suffers. Consequently, the obituary
can limit itself in the main to the communicating of
thoughts which have played a considerable role in my
endeavors. A theory is the more impressive the greater
the simplicity of its premises is, the more different kinds
of things it relates, and the more extended is its area of
applicability. Therefore the deep impression which classi-
cal thermodynamics made upon me. It is the only physical
theory of universal content concerning which I am con-
vinced that, within the framework of the applicability
of its basic concepts, it will never be overthrown (for the
special attention of those who are skeptics on principle).

The most fascinating subject at the time that I was a
student was Maxwell's theory. What made this theory
appear revolutionary was the transition from forces at a
distance to fields as fundamental variables. The incor-
poration of optics into the theory of electromagnetism,
with its relation of the speed of light to the electric and
magnetic absolute system of units as well as the relation
of the refraction coefficient to the dielectric constant,
the qualitative relation between the reflection coefficient
and the metallic conductivity of the body — it was like a
revelation. Aside from the transition to field-theory, i.e.,
the expression of the elementary laws through differential
equations, Maxwell needed only one single hypothetical
step — the introduction of the electrical displacement cur-
rent in the vacuum and in the dielectrica and its magnetic
effect, an innovation which was almost prescribed by the
formal properties of the differential equations.

What rendered the insight into the essence of electro-
magnetic theory so much more difficult at that time was
the following peculiar situation. Electric or magnetic
*'field intensities" and "displacements" were treated as
equally elementary variables, empty space as a special
instance of a dielectric body. Matter appeared as the
bearer of the field, not space. By this it was implied that
the carrier of the field could have velocity, and this
was naturally to apply to the "vacuum" (ether) also.
Hertz's electrodynamics of moving bodies rests entirely
upon this fundamental attitude.

It was the great merit of H. A. Lorentz that he brought
about a change here in a convincing
fashion. In principle a field exists, ac-
cording to him, only in empty space.
Matter— considered as atoms — is the
only seat of electric charges; between
the material particles there is empty
space, the seat of the electromag-
netic field, which is created by the
position and velocity of the point
charges which are located on the
material particles. Dielectricity, con-
ductivity, etc., are determined ex-
clusively by the type of mechanical
tie connecting the particles, of which
the bodies consist. The particle-
charges create the field, which, on
the other hand, exerts forces upon
the charges of the particles, thus de-
termining the motion of the latter
according to Newton's law of mo-
tion. If one compares this with
Newton's system, the change con-
sists in this: action at a distance is

also describes the radiation. Gravitation is usually not
taken into account because of its relative smallness; its
consideration, how^ever, was always possible by means
of the enrichment of the structure of the field, i.e., expan-
sion of Maxwell's law of the field. The physicist of the
present generation regards the point of view achieved by
Lorentz as the only possible one; at that time, however, it
was a surprising and audacious step, without which the
later development would not have been possible.

If one views this phase of the development of theory
critically, one is struck by the dualism which lies in
the fact that the material point in Newton's sense and
the field as continuum are used as elementary concepts
side by side. Kinetic energy and field-energy appear as
essentially different things. This appears all the more
unsatisfactory inasmuch as, according to Maxwell's the-
ory, the magnetic field of a moving electric charge repre-
sents inertia. Why not then total inertia? Then only
field-energy would be left, and the particle would be
merely an area of special density of field-energy. In
that case one could hope to deduce the concept of the
mass-point together with the equations of the motion
of the particles from the field equations—the disturbing
dualism would have been removed.

H. A. Lorentz knew this very well. However, Max-
well's equations did not permit the derivations of the
equilibrium of the electricity which constitutes a par-
ticle. Only other, nonlinear field equations could possibly
accomplish such a thing. But no method existed by
which this kind of field equations could be discovered
without deteriorating into adventurous arbitrariness. In
any case one could believe it possible by and by to find a
new and secure foundation for all of physics upon the
path so successfully begun by Faraday and Maxwell.

Accordingly, the revolution begun by the introduction
of the field was by no means finished. Then it happened
that, around the turn of the century, independently of
what we have just been discussing, a second fundamental
crisis set in, the seriousness of which was suddenly
recognized due to Max Planck's investigations into heat
radiation (1900).

My own interest in those years was less concerned
with the detailed consequences of Planck's results, how-
ever important these might be. My major question was:
what general conclusions can be drawn from the radia-
tion-formula concerning the structure of radiation and
(Continued on page 36)

-International News Service.

replaced by the field, which thus

Einstein's arrival in New York on a visit in 1921.

12

The Saturdav P^iew

NOTES FOR AN AUTOBIOGRAPHY

(Continued from page 12)

even more generally concerning the
electromagnetic foundation of phys-
ics?

Before I take this up I must briefly
mention a number of investigations
which relate to the Brownian motion
and related objects (fluctuation-phe-
nomena) and which in essence rest
upon classical molecular mechanics.
Not acquainted with the earlier inves-
tigations of Boltzmann and Gibbs,
which had appeared earlier and ac-
tually exhausted the subject, I devel-
oped the statistical mechanics and the
molecular-kinetic theory of therm-
odynamics which was based on the
former. My major aim in this was to
find facts which would guarantee as
much as possible the existence of
atoms of definite finite size.

In the midst of this I discovered
that, according to atomistic theory,
there would have to be a movement
of suspended microscopic particles
open to observation, without knowing
that observations concerning the
Brownian motion were already long
familiar. The simplest derivation
rested upon the following considera-
tion. If the molecular -kinetic theory
is essentially correct, a suspension of
visible particles must possess the same
kind of osmotic pressure fulfilling the
laws of gases as a solution of mole-
cules. This osmotic pressure depends
upon the actual magnitude of the
molecules, i.e., upon the number of
molecules in a gramequivalent. If the
density of the suspension is inhomo-
geneous, the osmotic pressure is in-
homogeneous, too, and gives rise to a
compensating diffusion, which can be
calculated from the well-known mo-
bility of the particles. This diffusion
can, on the other hand, also be con-
sidered as the result of the random
displacement — unknown in magnitude
originally — of the suspended particles
due to thermal agitation. By compar-
ing the amounts obtained for the
diffusion current from both types of
reasoning one reaches quantitatively
the statistical law for those displace-
ments, i.e., the law of the Brownian
motion. The agreement of these con-
siderations with experience together
with Planck's determination of the
true molecular size from the law of
radiation (for high temperatures)
convinced the skeptics, who were
quite numerous at that time (Ost-
wald, Mach), of the reality of atoms.
The antipathy of these scholars to-
wards atomic theory can indubitably
be traced back to their positivistic
philosophical attitude.

This is an interesting example of
the fact that even scholars of auda-
cious spirit and fine instinct can be
obstructed in the interpretation of
facts by philosophical prejudices. The
prejudice — which has by no means
died out in the meantime — consists in
the faith that facts by themselves can
and should yield scientific knowledge
without free conceptual construction.
Such a misconception is possible only
because one does not easily become
aware of the free choice of such con-
cepts, which, through verification and
long usage, appear to be immediately
connected with the empirical mate-
rial.

REFLECTIONS of this type made it
clear to me as long ago as short-
ly after 1900, i.e., shortly after
Planck's trail-blazing work, that
neither mechanics nor thermodynam-
ics could (except in limiting cases)
claim exact validity. By and by I des-
paired of the possibility of discovering
the true laws by means of construc-
tive efforts based on known facts. The
longer and the more despairingly I

tried, the more I came to the convic-
tion that only the discovery of a uni-
versal formal principle could lead us
to assured results. The example I saw
before me was thermodynamics. The
general principle was there given in
the theorem: the laws of nature are
such that it is impossible to construct
a perpetuum mobile (of- the first and
second kind). How, then, could such
a universal principle be found? After
ten years of reflection such a principle
resulted from a paradox upon which
I had already hit at the age of six-
teen: if I pursue a beam of light with
the velocity c (velocity of light in a
vacuum), I should observe such a
beam of light as a spatially oscilla-
tory electromagnetic field at rest.
However, there seems to be no such
thing, whether on the basis of experi-
ence or according to Maxwell's equa-
tions. From the very beginning it
appeared to me intuitively clear that,
judged from the standpoint of such
an observer, everything would have to
happen according to the same laws
as for an observer who, relative to
the earth, was at rest. For how,
otherwise, should the first observer
know, i.e., be able to determine, that
he is in a state of fast uniform mo-
tion?

One sees that in this paradox the

Your Literary L Q.

By Howard Collins

MORE GILBERT & SULLIVAN

L. L. Emery, of Durham Center, Conn., submits quotations in which various
G & S characters identify themselves in songs or remarks. Can you also iden-
tify them? Allowing four points for each correct answer, a score of sixty is
par, seventy-two is very good, and eighty or better is excellent. Answers are
on page 46.

1. "I am a mad wag — the merriest dog that barks.'*

2. "I am in reasonable health, and happy to meet you all once more."

3. "I think I am sufficiently decayed."

4. *Tm an everyday young man."

5. "I'm afraid I'm not equal to the intellectual pressure of the conversation."

6. "I am a maiden, cold and stately."

7. "A king of autocratic power we."

8. "I can trick you into learning with a laugh."

9. "I am an intellectual chap."

10. "I can write a washing bill in Babylonic cuneiform."

11. "Ah! bitter is my lot!"

12. "To indulge my lamentation no occasion do I miss."

13. "I smoke like a furnace, I'm always in liquor."

14. "The lark and the clerk, I remark, comfort me not."

15. "I always eat peas with a knife."

16. "My nature is love and light."

17. "I was born sneering."

18. "I once was as meek as a new-born lamb."

19. "I'm the slave of the gods, neck and heels."

20. "I find my duty hard to do today."

21. "I went to the bar as a very young man."

22. "And many a burglar Fve restored to his friends and his relations."

23. "I respect your Republican fallacies."

24. "I can tell a woman's age in half a minute."

25. "I do not care for dirty greens, by any means."

germ of the special relativity theory
is already contained. Today everyone
knows, of course, that all attempts to
clarify this paradox satisfactorily
were condemned to failure as long
as the axiom of the absolute charac-
ter of time, viz,, of simultaneity, un-
recognizedly was anchored in the
unconscious. Clearly to recognize this
axiom and its arbitrary character
really implies already the solution of
the problem. The type of critical
reasoning which was required for the
discovery of this central point was
decisively furthered, in my case
especially, by the reading of David
Hume's and Ernst Mach's philo-
sophical writings.

ONE had to understand clearly what
the spatial coordinates and the
temporal duration of events meant in
physics. The physical interpretation
of the spatial coordinates presupposed
a fixed body of reference, which,
moreover, had to be in a more or less
definite state of motion (inertial sys-
tem). In a given inertial system the
coordinates meant the results of cer-
tain measurements with rigid (sta-
tionary) rods. (One should always be
conscious of the fact that the pre-
supposition of the existence in prin-
ciple of rigid rods is a presupposition
suggested by approximate experience,
but which is, in principle, arbitrary.)
With such an interpretation of the
spatial coordinates the question of
the validity of Euclidean geometry
becomes a problem of physics.

If, then, one tries to interpret the
time of an event analogously, one
needs a means for the measurement
of the difference in time (in itself
determined periodic process realized
by a system of sufficiently small spa-
tial extension) . A clock at rest rela-
tive to the system of inertia defines
a local time. The local times of all
space points taken together are the
**time," which belongs to the selected
system of inertia, if a means is given
to "set" these clocks relative to each
other. One sees that a priori it is not
at all necessary that the /'times" thus
defined in different inertial systems
agree with one another. One would
have noticed this long ago, if, for the
practical experience of everyday life
light did not appear (because of the
high value of c), as the means for
the statement of absolute simul-
taneity.

The presupposition of the existence
(in principle) of (ideal, viz., perfect)
measuring rods and clocks is not in-
dependent of each other; since a
lightsignal, which is reflected back
and forth between the ends of a
rigid rod, constitutes an ideal clock,
provided that the postulate of the

constancy of the light-velocity in
vacuum does not lead to contradic-
tions.

The above paradox may then be
formulated as follows. According to
the rules of connection, used in
classical physics, of the spatial co-
ordinates and of the time of events
in the transition from one inertia!
system to another the two assump-
tions of

(1) the constancy of the light
velocity

(2) the independence of the laws
(thus specially also of the law
of the constancy of the light
velocity) of the choice of the
inertial system (principle of
special relativity)

are mutually incompatible (despite
the fact that both taken separately
are based on experience).

The insight which is fundamental
for the special theory of relativity is
this: the assumptions (1) and (2)
are compatible if relations of a new
type ("Lorentz- transformation") are
postulated for the conversion of co-
ordinates and the times of events.
With the given physical interpreta-
tion of coordinates and time, this is
by no means merely a conventional
step, but implies certain hypotheses
concerning the actual behavior of
moving measuring-rods and clocks,
which can be experimentally vali-
dated or disproved.

The universal principle of the spe-
cial theory of relativity is contained
in the postulate: the laws of physics
are invariant with respect to the
Lorentz-transformations (for the
transition from one inertial system
to any other arbitrarily chosen sys-
tem of inertia). This is a restricting
principle for natural laws, compar-
able to the restricting principle of
the non-existence of the perpetuum
mobile which underlies thermody-
namics.

First a remark concerning the
relation of the theory to "four-di-
mensional space." It is a widespread
error that the special theory of rela-
tivity is supposed to have, to a cer-
tain extent, first discovered, or at any
rate, newly introduced, the four-
dimensionality of the physical con-
tinuum. This, of course, is not the
case. Classical mechanics, too, is
based on the four-dimensional con-
tinuum of space and time. But in the
four-dimensional continuum of classi-
cal physics the subspaces with con-
stant time value have an absolute
reality, independent of the choice of
the reference system. Because of this
[fact], the four-dimensional con-
tinuum falls naturally into a three- i
dimensional and a one-dimensional I
(time), so that the four-dimensional I

point of view does not force itself
upon one as necessary. The special
theory of relativity, on the other
hand, creates a formal dependence
between the way in which the spatial
coordinates, on the one hand, and the
temporal coordinates, on the other,
have to enter into the natural laws.

MINKOWSKI'S important contri-
bution to the theory lies in the
following: before Minkowski's inves-
tigation it was necessary to carry out
a Lorentz-transformation on a law in
order to test its invariance under such
transformations; he, on the other
hand, succeeded in introducing a for-
malism such that the mathematical
form of the law itself guarantees its
invariance under Lorentz-transforma-
tions. By creating a four-dimensional
tensor-calculus he achieved the same
thing for the four-dimensional space
which the ordinary vector-calculus
achieves for the three spatial dimen-
sions. He also showed that the Lor-
entz-transformation (apart from a
different algebraic sign due to the
special character of time) is nothing
but a rotation of the coordinate sys-
tem in the four-dimensional space.

First, a remark concerning the
theory as it is characterized above.
One is struck [by the fact] that the
theory (except for the four-dimen-
sional space) introduces two kinds of
physical things, i.e., (1) measuring
rods and clocks, (2) all other things,
e.g., the electro-magnetic field, the
material point, etc. This, in a certain
sense, is inconsistent; strictly speaking
m.easuring rods and clocks would
have to be represented as solutions
of the basic equations (objects con-
sisting of moving atomic configura-
tions), not, as it were, as theoretically
self-sufficient entities. However, the
procedure justifies itself because it
was clear from the very beginning
that the postulates of the theory are
not strong enough to deduce from
them sufficiently complete equations
for physical events sufficiently free
from arbitrariness, in order to base
upon such a foundation a theory of
measuring rods and clocks. If one did
not wish to forego a physical inter-
pretation of the coordinates in gen-
eral (something which, in itself,
would be possible), it was better to
permit such inconsistency — with the
obligation, however, of eliminating it
at a later stage of the tiieory. But
one must not legalize the mentioned
sin so far as to imagine that inter-
vals are physical entities of a special
type, intrinsically different from
other physical variables ("reducing
physics to geometry," etc.).

We now shall inquire into the in-
sights of definite nature which phys-

ics owes to the special theory of
relativity.

(1) There is no such thing as si-
multaneity of distant events; conse-
quently there is also no such thing
as immediate action at a distance in
the sense of Newtonian mechanics.
Although the introduction of actions
at a distance, which propagate with
the speed of light, remains thinkable,
according to this theory, it appears
unnatural; for in such a theory there
could be no such thing as a reason-
able statement of the principle of
conservation of energy. It therefore
appears unavoidable that physical
reality must be described in terms
of continuous functions in space. The
material point, therefore, can hardly
be conceived any more as the basic
concept of the theory.

(2) The principles of the conserva-
tion of momentum and of the con-
servation of energy are fused into
one single principle. The inert mass
of a closed system is identical with
its energy, thus eliminating mass as
an independent concept.

Remark. The speed of light c is one
of the quantities which occurs as
"universal constant" in physical
equations. If, however, one introduces
as unit of time instead of the second
the time in which light travels 1 cm,
c no longer occurs in the equations.
In this sense one could say that the
constant c is only an apparently uni-
versal constant.

It is obvious and generally accepted
that one could eliminate two more
universal constants from physics by
introducing, instead of the gram and
the centimeter, properly chosen **nat-
ural" units (for example, mass and
radius of the electron) .

If one considers this done, then
only "dimension-less" constants could
occur in the basic equations of phys-
ics. Concerning such I would like to
state a theorem which at present can-
not be based upon anything more
than upon a faith in the simplicity,
i.e., intelligibility, of nature: there
are no arbitrary constants of this
kind; that is to say, nature is so con-
stituted that it is possible logically to
lay down such strongly determined
laws that within these laws only ra-
tionally completely determined con-
stants occur (not constants, therefore,
whose numerical value could be
changed without destroying the
theory).

The special theory of relativity
owes itS" origin to Maxwell's equations
of the electromagnetic field. Inversely
the latter can be grasped formally in
satisfactory fashion only by way of
the special theory of relativity. Max-
wells equations are the simplest
L o r e n t z-invariant field equations

which can be postulated for an anti-
symmetric tensor derived from a vec-
tor field. This in itself would be sat-
isfactory, if we did not know from
quantum phenomena that Maxwell's
theory does not do justice to the
energetic properties of radiation. But
how Maxwell's theory would have to
be modified in a natural fashion, for
this even the special theory of rela-
tivity offers no adequate foothold.
Also to Mach's question: "How does
it come about that inertial systems
are physically distinguished above
all other coordinate systems?" this
theory offers no answer.

That the special theory of relativ-
ity is only the first step of a necessary
development became completely clear
to me only in my efforts to represent
gravitation in the framework of this
theory. In classical mechanics, inter-
preted in terms of the field, the po-
tential of gravitation appears as a
scalar field (the simplest theoretical
possibility of a field with a single
component). Such a scalar theory of
the gravitational field can easily be
made invariant under the group of
Lorentz-transformations. The follow-
ing program appears natural, there-
fore: the total physical field consists
of a scalar field (gravitation) and a
vector field (electromagnetic field) ;
later insights may eventually make
necessary the introduction of still
more complicated types of fields; but
to begin with one did not need to
bother about this.

The possibility of the realization of
this program was, however, dubious
from the very first, because the
theory had to combine the following
things:

(1) From the general considera-
tions of special relativity
theory it was clear that the
inert mass of a physical system
increases with the total energy
(therefore, e.g., with the ki-
netic energy).

(2) From very accurate experi-
ments (specially from the tor-
sion balance experiments of
Eotvos) it was empirically
known with very high accur-
acy that the gravitational mass
of a body is exactly equal to
its inert mass.

It followed from (1) and
(2) that the weight of a sys-
tem depends in a precisely
known manner on its total
energy. If the theory did not
accomplish this or could not
do it naturally, it was to be
rejected. The condition is most
naturally expressed as fol-
lows: the acceleration of a
system falling freely in a
given gravitational field is in-
dependent of the nature of the
falling system (specially
therefore also of its energy
content) .

It then appeared that in the frame-
work of the program sketched this
elementary state of affairs could not
at all or at any rate not in any nat-
ural fashion, be represented in a sat-
isfactory way. This convinced me that
within the frame of the special theory
of relativity there is no room for a
satisfactory theory of gravitation.

Now it came to me: the fact of
the equality of inert and heavy mass,
i.e., the fact of the independence of
the gravitational acceleration of the
nature of the falling substance, may
be expressed as follows: in a gravi-
tational field (of small spatial exten-
sion) things behave as they do in a
space free of gravitation, if one in-
troduces in it, in place of an "inertial
system,'* a reference system which is
accelerated relative to an inertial sys-
tem.

If then one conceives of the be-
havior of a body, in reference to the
latter reference system, as caused by
a **rear' (not merely apparent)
gravitational field, it is possible to
regard this reference system as an
"inertial system" with as much justi-
fication as the original reference sys-
tem.

So, if one regards as possible, gravi-
tational fields of arbitrary extension
which are not initially restricted by
spatial limitations, the concept of the
"inertial system" becomes completely
empty. The concept, "acceleration
relative to space," then loses every
meaning and with it the principle of
inertia together with the entire para-
dox of Mach.

The fact of the equality of inert
and heavy mass thus leads quite nat-
urally to the recognition that the
basic demand of the special theory
of relativity (invariance of the laws
under Lorentz-transformations) is too
narrow, i.e., that an invariance of the
laws must be postulated also relative
to non-linear transformations of the
coordinates in the four-dimensional
continuum.

This happened in 1908. Why were
another seven years required for the
construction of the general theory of
relativity? The main reason lies in
the fact that it is not so easy to free
oneself from the idea that coordinates
rnust have an immediate metrical
meaning. The transformation took
place in approximately the following
fashion.

We start with an empty, field-free
space, as it occurs — related to an in-
ertial system — in the sense of the spe-
cial theory of relativity, as the
simplest of all imaginable physical
situations. If we now think of a non-
inertial system introduced by assum-
ing that the new system is uniformly

accelerated against the inertial sys-
tem (in a three-dimensional descrip-
tion) in one direction (conveniently
defined) , then there exists with ref-
erence to this system a static parallel
gravitational field. The reference
system may thereby be chosen as
rigid, of Efuclidian type, in three-
dimensional metric relations. But the
time, in which the field appears as
static, is not measured by equally
constituted stationary clocks. From
this special example one can already
recognize that the immediate metric
significance of the coordinates is lost
if one admits non-linear transforma-
tions of coordinates at all. To do the
latter is, however, obligatory if one
wants to do justice to the equality
of gravitational and inert mass by
means of the basis of the theory, and
if one wants to overcome Mach's
paradox as concerns the inertial sys-
tems.

If, then, one must give up the
attempt to give the coordinates an
immediate metric meaning (differ-
ences of coordinates = measurable
lengths, viz., times), one will not be
able to avoid treating as equivalent
all coordinate systems, which can be
created by the continuous transform-
ations of the coordinates.

The general theory of relativity,
accordingly, proceeds from the fol-
lowing principle: natural laws are
to be expressed by equations which
are covariant under the group of con-
tinuous coordinate transformations.
This group replaces the group of the
Lorentz-transformations of the spe-
cial theory of relativity, which forms
a sub-group of the former.

If anything in the theory as
sketched — apart from the demand of
the invariance of the equations un-
der the group of the continuous co-
ordinate-transformations — c a n pos-
sibly make the claim to final
significance, then it is the theory of
the limiting case of the pure gravita-
tional field and its relation to the
metric structure of space. For this
reason, in what immediately follows
we shall speak only of the equations
of the pure gravitational field.

The peculiarity of these equations
lies, on the one hand, in their com-
plicated construction, especially their
non-linear character as regards the
field -variables and their derivatives,
and, on the other hand, in the almost
compelling necessity with which the
transformation-group determines this
complicated field-law. If one had
stopped with the special theory of
relativity, i.e., with the invariance
under the Lorentz-group, then the
field-law R.j^ — o would remain invar-
iant also within the frame of this
narrower group. But from the point

of view of the narrower group there
would at first exist no reason for rep-
resenting gravitation by so compli-
cated a structure as is represented by
the symmetric tensor g.^. It, nonethe-
less, one would find sufficient reasons
for it, there would then arise an im-
mense number of field-laws out of
quantities g.^^ all of which are covar-
iant under Lorentz-transformations
(not, however, under the general
group). However, even if, of all the
conceivable Lorentz-invariant laws,
one had accidentally guessed precise-
ly the law which belongs to the wider
group, one would still not be on
the plane of insight achieved by the
general principle of relativity. For,
from the standpoint of the Lorentz-
group two solutions would incorrectly
have to be viewed as physically dif-
ferent from each other, if they can
be transformed into each other by a
non-linear transformation of coordi-
nates, i.e., if they are, from the point
of view of the wider field, only dif-
ferent representations of the same
field.

I must take a stand with reference
to the most successful physical
theory of our period, viz., the statis-
tical quantum theory which, about
twenty-five years ago, took on a con-
sistent logical form (Schrodinger,
Heisenberg, Dirac, Born) . This is the
only theory at present which permits
a unitary grasp of experiences con-
cerning the quantum character of
micro-mechanical events. This theory,
on the one hand, and the theory of
relativity on the other, are both con-
sidered correct in a certain sense, al-
though their combination has resisted
all efforts up to now. This is probably
the reason why among contemporary
theoretical physicists there exist en-
tirely differing opinions concerning
the question as to how the theoreti-
cal foundation of the physics of the
future will appear. Will it be a field
theory; will it be in essence a statis-
tical theory? I shall briefly indicate
my own thoughts on this point.

Physics is an attempt conceptually
to grasp reality as it is thought inde-
pendently of its being observed. In
this sense one speaks of ''physical
reality." In pre-quantum physics
there was no doubt as to how this
was to be understood. In Newton's
theory reality was determined by a
material point in space and time; in
Maxwell's theory, by the field in
space and time. In quantum me-
chanics it is not so easily seen.

This exposition has fulfilled its
purpose if it shows the reader how
the efforts of a life hang together
and why they have led to expecta-
tions of a definite form.